# Triangular Inequality – building the triangle

Change the measurements of the segments and look at the triangle. Will it exist, regardless of segment size?

In the next structure, check the "Hide / Show sum of triangle side measures" and "Hide / show sum of segment measurements" boxes. Change the measurements of the segments, look at the sums and measurements of the sides.

From what you have noticed, in what condition(s) does the triangle exists?

## Build the triangle with the compass

Using the compass, build a triangle whose sides have the measurements of segments AB, CD, and EF.

## Properties

1-The longest side is opposite the largest angle. In other words, if two sides of a triangle are not congruent, then the angles opposite them are not congruent and the side opposite to the larger angle is the longer side (search for a demonstration for this).  2- The largest angle is opposite the longest side. In other words, if two sides of a triangle are not congruent, then the angles opposite them are not congruent and the angle opposite to the longer side is the larger angle (search for a demonstration for this).

## Analysis

Did you understand the proof? If you did not understand, enter your question here.